The theorem of Riemann-Roch

  • André Weil
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 144)


The classical theory of algebraic number-fields, as described above in Chapter V, rests upon the fact that such fields have a non-empty set of places, the infinite ones, singled out by intrinsic properties. It would be possible to develop an analogous theory for A-fields of characteristic p >1 by arbitrarily setting apart a finite number of places; this was the point of view adopted by Dedekind and Weber in the early stages of the theory. Whichever method is followed, the study of such fields leads very soon to results which cannot be properly understood without the use of concepts belonging to algebraic geometry; this lies outside the scope of this book. The results to be given here should be regarded chiefly as an illustration for the methods developed above and as an introduction to a more general theory.


Finite Field Haar Measure Compact Subgroup Dual System Coherent System 
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Copyright information

© Springer Science+Business Media New York 1973

Authors and Affiliations

  • André Weil
    • 1
  1. 1.The Institute for Advanced StudyPrincetonUSA

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